Police said it was a "tactical option" after more than 50 sightings of the device near the airfield since Wednesday night when the runway was first closed.
Police and airport authorities believe the drone is being flown in a deliberate act to disrupt the airport at one of the busiest times of year, leaving tens of thousands of passengers stranded just days before Christmas.
On Thursday Britain called in the army to offer additional support to police as they hunt for those responsible.
"We will do what we can to take that drone out of the sky and remove that disruption so we can get Gatwick back to normal," Detective Chief Superintendent Jason Tingley said, despite earlier concerns that shooting the drone would be dangerous due to the danger of stray bullets.
"One of the options is to use firearms officers if that presents itself -- they have been out on the ground today and that's a consideration and a tactical option that's open to us."
He said he believed the drone had been modified with the "intent of causing disruption" and were looking through CCTV to identify the make and model.
The airport said late Thursday its only runway could not be reopened following further appearances of the drone.
"Gatwick's runway remains unavailable because of continued drone sightings," it said.
Specialist equipment has been deployed by the MOD (Ministry of Defence) to Gatwick airport to assist Sussex Police.
"We are there to assist and do everything we can," Defence Secretary Gavin Williamson told Sky News television, declining to give the troops' exact role and adding that it followed a request from local police.
- 'It's childish' -
Gisele Fenech, 43, who was travelling to Malta, was among those stranded at the airport.
"We're meeting family and it's my daughter's birthday today so it's gone all wrong. We've been looking forward to this for so long," she told AFP.
"Everyone's trying to get home for Christmas."
Gatwick, around 30 miles (50 kilometres) south of the British capital, is the eighth-busiest airport in Europe and sits behind Mumbai as the world's busiest single runway air hub.
Inbound flights were diverted to other airports, including Paris, while passengers waiting to take off faced gruelling delays as airlines cut services.
Transport Secretary Chris Grayling said overnight restrictions would be lifted at some airports to help ease the situation.
Some 10,000 passengers were affected on Wednesday night, and a further 110,000 who had been due to either take off or land at the airport on 760 flights Thursday.
Musab Rashid, 22, who was going to Copenhagen, said: "It's wrong, it's childish of them to do this, because it's affected more than 100,000 people."
- Cat-and-mouse manhunt -
Two drones were first spotted flying over Gatwick at around 9pm (2100 GMT) on Wednesday. The airfield briefly reopened at 3am on Thursday, but had to be closed again following further sightings through the day.
Gatwick CEO Stewart Wingate said the incident was "a highly targeted activity which has been designed to close the airport and bring maximum disruption in the run up to Christmas".
"We are working very closely with the police and the security services to try to resolve this for passengers," he said, adding "as soon as we can we will" reopen the runway.
A cat-and-mouse manhunt is under way to catch those operating the drones, with more than 20 police units and dozens of officers from two local forces deployed.
"Each time we believe we get close to the operator, the drone disappears; when we look to reopen the airfield, the drone reappears," said police superintendent Justin Burtenshaw on Thursday, adding there were no indication the incident was terror-related.
British Prime Minister Theresa May said she sympathised with passengers and vowed action.
"We will continue to work with the Gatwick authorities and police will be working... in order to bring this to a close," she told a press conference in London.
Under a new British law, drones cannot be flown near aircraft or within a kilometre of an airport, or at an altitude of over 400 feet (122 metres).
May warned the perpetrators they could face up to five years in prison for endangering an aircraft under recently passed legislation.
"We're consulting on further aspects of this including further police powers," she added.
Gatwick serves more than 228 destinations in 74 countries for 45 million passengers a year.